# The value of lim v → 4 + ( 4 − v | 4 − v | ) . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2, Problem 10RE
To determine

## To find: The value of limv→4+(4−v|4−v|).

Expert Solution

The limit of the function is −1.

### Explanation of Solution

Definition used:

An absolute function |x| is defined as follows.

|x|={x if x<0x if x0

Direct substitution property:

If f is a polynomial or a rational function and a is in the domain of f, then limxaf(x)=f(a).

Calculation:

Let f(v)=4v|4v|.

Use the definition of absolute value function to define the function |4v|,

|4v|={4vif 4v0(4v)if 4v<0={4vif v4(4v)if v>4

Since f(v)=4v(4v) for v>4,

limv4+(4v|4v|)=limv4+(4v(4v))=limv4+(4v(4v))=limv4+(1)=1[by direct substitution]

Thus, the limit of the function is −1.

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